TY - JOUR

T1 - Non-Orthogonal Opportunistic Beamforming: Performance Analysis and Implementation

AU - Xia, Minghua

AU - Wu, Yik-Chung

AU - Aissa, Sonia

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2012/2/13

Y1 - 2012/2/13

N2 - Aiming to achieve the sum-rate capacity in multi-user multi-antenna systems where $N_t$ antennas are implemented at the transmitter, opportunistic beamforming (OBF) generates~$N_t$ orthonormal beams and serves $N_t$ users during each channel use, which results in high scheduling delay over the users, especially in densely populated networks. Non-orthogonal OBF with more than~$N_t$ transmit beams can be exploited to serve more users simultaneously and further decrease scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between sum-rate and scheduling delay for non-orthogonal OBF. In this context, system performance and implementation of non-orthogonal OBF with $N>N_t$ beams are investigated in this paper. Specifically, it is analytically shown that non-orthogonal OBF is an interference-limited system as the number of users $K \to \infty$. When the inter-beam interference reaches its minimum for fixed $N_t$ and~$N$, the sum-rate scales as $N\ln\left(\frac{N}{N-N_t}\right)$ and it degrades monotonically with the number of beams $N$ for fixed $N_t$. On the contrary, the average scheduling delay is shown to scale as $\frac{1}{N}K\ln{K}$ channel uses and it improves monotonically with $N$. Furthermore, two practical non-orthogonal beamforming schemes are explicitly constructed and they are demonstrated to yield the minimum inter-beam interference for fixed $N_t$ and $N$. This study reveals that, if user traffic is light and one user can be successfully served within a single transmission, non-orthogonal OBF can be applied to obtain lower worst-case delay among the users. On the other hand, if user traffic is heavy, non-orthogonal OBF is inferior to orthogonal OBF in terms of sum-rate and packet delay.

AB - Aiming to achieve the sum-rate capacity in multi-user multi-antenna systems where $N_t$ antennas are implemented at the transmitter, opportunistic beamforming (OBF) generates~$N_t$ orthonormal beams and serves $N_t$ users during each channel use, which results in high scheduling delay over the users, especially in densely populated networks. Non-orthogonal OBF with more than~$N_t$ transmit beams can be exploited to serve more users simultaneously and further decrease scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between sum-rate and scheduling delay for non-orthogonal OBF. In this context, system performance and implementation of non-orthogonal OBF with $N>N_t$ beams are investigated in this paper. Specifically, it is analytically shown that non-orthogonal OBF is an interference-limited system as the number of users $K \to \infty$. When the inter-beam interference reaches its minimum for fixed $N_t$ and~$N$, the sum-rate scales as $N\ln\left(\frac{N}{N-N_t}\right)$ and it degrades monotonically with the number of beams $N$ for fixed $N_t$. On the contrary, the average scheduling delay is shown to scale as $\frac{1}{N}K\ln{K}$ channel uses and it improves monotonically with $N$. Furthermore, two practical non-orthogonal beamforming schemes are explicitly constructed and they are demonstrated to yield the minimum inter-beam interference for fixed $N_t$ and $N$. This study reveals that, if user traffic is light and one user can be successfully served within a single transmission, non-orthogonal OBF can be applied to obtain lower worst-case delay among the users. On the other hand, if user traffic is heavy, non-orthogonal OBF is inferior to orthogonal OBF in terms of sum-rate and packet delay.

UR - http://hdl.handle.net/10754/251674

UR - http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6151774

UR - http://www.scopus.com/inward/record.url?scp=84862829067&partnerID=8YFLogxK

U2 - 10.1109/TWC.2012.020812.110311

DO - 10.1109/TWC.2012.020812.110311

M3 - Article

SN - 1536-1276

VL - 11

SP - 1424

EP - 1433

JO - IEEE Transactions on Wireless Communications

JF - IEEE Transactions on Wireless Communications

IS - 4

ER -